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A327828 Sum of multinomials M(n; lambda), where lambda ranges over all partitions of n into parts incorporating 2.

%I A327828 #10 Dec 18 2020 04:01:56
%S A327828 0,0,1,3,18,100,705,5166,44856,413316,4297635,47906650,586050828,
%T A327828 7669704978,108433645502,1632017808435,26240224612920,446861879976600,
%U A327828 8063224431751719,153335328111105282,3070484092409318100,64508501542986638550,1420061287311444508962
%N A327828 Sum of multinomials M(n; lambda), where lambda ranges over all partitions of n into parts incorporating 2.
%H A327828 Alois P. Heinz, <a href="/A327828/b327828.txt">Table of n, a(n) for n = 0..450</a>
%F A327828 a(n) ~ c * n!, where c = A247551/2 = 1.26473873603957632409005807712697712... - _Vaclav Kotesovec_, Sep 28 2019
%p A327828 b:= proc(n, i, k) option remember; `if`(n=0, 1,
%p A327828      `if`(i>n, 0, b(n, i+1, `if`(i=k, 0, k))+
%p A327828      `if`(i=k, 0, b(n-i, i, k)*binomial(n, i))))
%p A327828     end:
%p A327828 a:= n-> b(n, 1, 0)-b(n, 1, 2):
%p A327828 seq(a(n), n=0..23);
%t A327828 b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i > n, 0, b[n, i + 1, If[i == k, 0, k]] + If[i == k, 0, b[n - i, i, k] Binomial[n, i]]]];
%t A327828 a[n_] := b[n, 1, 0] - b[n, 1, 2];
%t A327828 a /@ Range[0, 23] (* _Jean-François Alcover_, Dec 18 2020, after _Alois P. Heinz_ *)
%Y A327828 Column k=2 of A327801.
%K A327828 nonn
%O A327828 0,4
%A A327828 _Alois P. Heinz_, Sep 26 2019